Structured Population Models

The chapter “Structured Population Models” illustrates how one adds more detail to a model, first through density-independent models, then by showing common matrix-model formulations and how those are used to reveal properties of structured models (e.g. population growth rate, stage/age structure). Structured population models have more detail than their nonstructured counterparts. They account for the differences among individuals within a population, usually by explicitly modeling them as distinct state variables. Elasticity analysis is introduced as a way to identify life stages that have a disproportionately large influence on population growth rate. Structured density-dependent models are briefly introduced as extensions on these models.

Skills for Dynamic Models

The chapter “Skills for Dynamic Models” provides worked examples of the dynamic models presented in Part 1, both in spreadsheets and in R. It also covers some of the mathematical steps used in model analysis. In most cases, instructions are given for both spreadsheets and R. However, when some activities are far easier to do in a programming environment than in spreadsheets, only the instructions for R are shown. The chapter starts out by discussing the skills needed for structured population models, including setting up age structure and creating cobweb plots. Next, it reviews the skills needed for multivariable models, including calculating isoclines and Jacobian matrices. Finally, it introduces the concept of Monte Carlo methods and provides guidance on how to implement them.

Spaces of Measures and their Applications to Structured Population Models

Structured population models are transport-type equations often applied to describe evolution of heterogeneous populations of biological cells, animals or humans, including phenomena such as crowd dynamics or pedestrian flows. This book introduces the mathematical underpinnings of these applications, providing a comprehensive analytical framework for structured population models in spaces of Radon measures. The unified approach allows for the study of transport processes on structures that are not vector spaces (such as traffic flow on graphs) and enables the analysis of the numerical algorithms used in applications. Presenting a coherent account of over a decade of research in the area, the text includes appendices outlining the necessary background material and discusses current trends in the theory, enabling graduate students to jump quickly into research.

Demographic processes in socially structured populations

In socially structured animal populations, vital rates such as survival and reproduction, are affected by complex interactions among individuals of different social ranks and among social groups. Due to this complexity, mechanistic approaches to model vital rates may be preferred over commonly used structured population models. However, mechanistic approaches come at a cost of increased modelling complexity, computational requirements, and reliance on simulated metrics, while structured population models are analytically tractable. This chapter compares different approaches to modelling population dynamics of socially structured populations. It first simulates individual-based data based on the life cycle of a hypothetical cooperative breeder and then projects population dynamics using a matrix population model (MPM), an integral projection model (IPM), and an individual-based model (IBM). The authors demonstrate that, when projecting population size or structure, the relatively simpler MPM can outperform both the IPM and IBM. However, mechanistic details parametrised in the more complex IBM are required to accurately project interactions within social groups. The R scripts in this chapter provide a roadmap to both simulate data that best describe a socially structured system and assess the level of model complexity needed to capture the dynamics of the system.